Morrey spaces norms and criteria for blowup in chemotaxis models

DOI10.3934/nhm.2016.11.239zbMath1333.35299OpenAlexW2313586387MaRDI QIDQ262146

Piotr Biler, Jacek Zienkiewicz, Grzegorz Karch

Publication date: 29 March 2016

Published in: Networks and Heterogeneous Media (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/nhm.2016.11.239

zbMATH Keywords

chemotaxisfractional diffusionblowup of solutionsparabolic-elliptic Keller-Segel model

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Second-order parabolic systems (35K40) Blow-up in context of PDEs (35B44)

Related Items (7)

Large global-in-time solutions to a nonlocal model of chemotaxis ⋮ Solutions to the Keller-Segel system with non-integrable behavior at spatial infinity ⋮ Blowing up radial solutions in the minimal Keller-Segel model of chemotaxis ⋮ Blowup versus global in time existence of solutions for nonlinear heat equations ⋮ Mathematical challenges in the theory of chemotaxis ⋮ Blow-up criteria for the classical Keller-Segel model of chemotaxis in higher dimensions ⋮ Global radial solutions in classical Keller-Segel model of chemotaxis

Cites Work

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• Existence of Solutions for the Keller–Segel Model of Chemotaxis with Measures as Initial Data
• Blow-up versus global existence of solutions to aggregation equations
• Optimal criteria for blowup of radial andN-symmetric solutions of chemotaxis systems
• Existence and nonexistence of solutions for a model of gravitational interaction of particles, III
• The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
• Two‐dimensional chemotaxis models with fractional diffusion
• Blowup of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains

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